Often called a linear motor or voice/speaker coil, the electromagnetic actuator is versatile and relatively easy to design/build.
Step 1: Design the Actuator You Have Always Wanted.
There are two ways to do this: you may either go through the attached voiceCoilEquations.pdf, find all my mistakes, and develop your own magnetic circuit model, OR you can download the attached solidworks files and excel spreadsheet and just use the parametric model I have built.
Step 2: Enter the Specifications
Solidworks comes with with this handy feature called a design table. It is an excel spread sheet which can, and in this case does, contain a bunch of equations that drive the design. So, open the spreadsheet - either in excel or in solidworks - and in the yellow hightlighed area, enter in the pertinent parameters: desired force, throw, lateral clearance, and magnet strength/geometry.
You will have to manipulate the gap height parameter to find the gap height that gives the best flux density (least power) while not exceeding whatever spatial limitations you might have. As you play with this, you will not that the equations break if you choose this parameter unusually low or high.
Step 3: Machine the Stator and Bobbin
After tweaking the design in solidworks, output some drawings and take them to the machine shop.
A couple of tips on this step. Machining a deep pocket in Iron (or soft steel) for the stator is a pain. As a alternative, you may machine a cylinder and a disc. Place the cylinder on a hot plate and the disc in ice water. After the cylinder is at 500 oF and the disc at 30 oF, slam them together using an arbor press (exciting). The bobbin should be made out of aluminum or plastic. Be careful while assembling the magnet and flux puck into the stator cup. It is recommended to machine a guide for the magnet and puck so as to avoid losing digits.
Step 4: Wind Bobbin
Scrolling to the bottom of the design table spreadsheet will reveal a number of wire guage choices. Hopefully, one of these will work with your amplifier.
Wind the magnet wire onto the bobbin. With either a lathe or a bobbin winding machine. Try to keep relatively constant tension on the wire as you wind the coil.
Wrap electrical tape around the finished windings or pot in epoxy.